Kosovo lost 6-0 to Croatia in their first competitive home fixture, which was played in neighbouring Albania.
The 2018 World Cup qualifier could not be held in Kosovo because of a lack of infrastructure, but thousands of fans made the trip to Shkoder.
Juventus striker Mario Mandzukic scored a first-half hat-trick for Croatia, who are top of qualifying Group I.
Matej Mitrovic, Ivan Perisic and Nikola Kalinic scored in the second half to leave Kosovo bottom of the group.
Governing bodies Uefa and Fifa admitted Kosovo as a member in May, and in September they drew their first competitive fixture 1-1 in Finland.
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